
iii
Preface
Over the years, when reviewing books we found that many had been mainstreamed by
the publishers in an effort to appeal to everyone, leaving them with very little character.
There were only a handful of books that had the conceptual and application driven focus
we liked, and most of those were lacking in other aspects we cared about, like providing
students sufficient examples and practice of basic skills. The largest frustration, however,
was the never ending escalation of cost and being forced into new editions every three
years. We began researching open textbooks, however the ability for those books to be
adapted, remixed, or printed were often limited by the types of licenses, or didn’t
approach the material the way we wanted.
This book is available online for free, in both Word and PDF format. You are free to
change the wording, add materials and sections or take them away. We welcome
feedback, comments and suggestions for future development at
precalc@opentextbookstore.com. Additionally, if you add a section, chapter or problems,
we would love to hear from you and possibly add your materials so everyone can benefit.
In writing this book, our focus was on the story of functions. We begin with function
notation, a basic toolkit of functions, and the basic operation with functions: composition
and transformation. Building from these basic functions, as each new family of functions
is introduced we explore the important features of the function: its graph, domain and
range, intercepts, and asymptotes. The exploration then moves to evaluating and solving
equations involving the function, finding inverses, and culminates with modeling using
the function.
The "rule of four" is integrated throughout - looking at the functions verbally,
graphically, numerically, as well as algebraically. We feel that using the “rule of four”
gives students the tools they need to approach new problems from various angles. Often
the “story problems of life” do not always come packaged in a neat equation. Being able
to think critically, see the parts and build a table or graph a trend, helps us change the
words into meaningful and measurable functions that model the world around us.
There is nothing we hate more than a chapter on exponential equations that begins
"Exponential functions are functions that have the form f(x)=a
x
." As each family of
functions is introduced, we motivate the topic by looking at how the function arises from
life scenarios or from modeling. Also, we feel it is important that precalculus be the
bridge in level of thinking between algebra and calculus. In algebra, it is common to see
numerous examples with very similar homework exercises, encouraging the student
to mimic the examples. Precalculus provides a link that takes students from the basic
plug & chug of formulaic calculations towards building an understanding that equations
and formulas have deeper meaning and purpose. While you will find examples and
similar exercises for the basic skills in this book, you will also find examples of multistep
problem solving along with exercises in multistep problem solving. Often times these
exercises will not exactly mimic the exercises, forcing the students to employ their
critical thinking skills and apply the skills they've learned to new situations. By